A Falcon 9 produces about 149 metric tons of carbon dioxide from launch. The US produced about 9.5 metric tons a second. In 16 seconds the US has produced the same amount of carbon as a Falcon 9 launch. I don't think that is terribly significant
Assuming you make your hydrogen purely by electrolyzing water, you still need a power source to do that. Unless your power source is carbon neutral, it doesn't make sense to say the hydrogen is.
Why do we care? That’s like being concerned about wood being used to build ships in the 15th century. The carbon footprint of all of the private jets that flew to the Paris Climate talks dwarfs anything put out by a rocket, yet were people interested in emissions suggesting WebEx instead?
I don’t think either rockets or private jets are worth fretting about when it comes to climate change, but I’ve seen a lot of people suggest that flying to compare conferences is hypocritical and everyone should just videoconference over the internet instead.